In Exercises 15–26, use graphs to find each set.

(- 3, 0) ⋃ [- 1...

Question

In Exercises 15–26, use graphs to find each set.

(- 3, 0) ⋃ [- 1, 2]

Accepted Answer

Hello. Everyone in this video, we're going to be looking at this practice problem where we want to find the union between the two intervals negative 5-1 and negative 3-4. So in this case we're going to do number line graphs to sort of visualize these intervals and help us find the union. So in this case I want to draw a number line that is wide enough to capture the lowest and the highest values of these ranges. So you can see that the highest is four and the lowest is negative five. So I want to make sure that my number line captures At least within the that range. So if I start at negative six and I number upwards, I'm gonna go three and then I'll add some length to go up to five And there's my four. So now I have a number line that captures my highest and lowest values listed on the ranges. So now I'm going to go ahead and draw my first range, which is bracket negative five Or parentheses -5 2, Parentheses one. So this is my first range or first interval and now I'm going to draw a second number line with the same amount of numbers as my first because I want to compare my first interval to my second interval. So if I do that, I have my second number line Representing my second interval and my second interval is bracket negative three two, bracket four. And you can see that this one goes a bit higher than my first one, Going up all the way to four And my first one goes lower than my second one, going all the way down to negative five. So I'm gonna draw a third number line using the same Numbering as my previous two. And I'm going to use this third number line to visualize where the union occurs or the range of values that captures both my first interval and my second interval. So here's my third Number line going again from -6-5. And we already said that my first interval goes lower than my second interval. So that represents my lower bound and it seems like the lower bound is at -5. So I'm gonna do parentheses negative five for that lower bound. And then we already stated that my second interval goes higher than my first interval, It goes up to four. So that becomes my upper bound for this range. So if I do a bracket for you can see that my red line captures both my first interval and my second interval. So this becomes my union. And if I represent the union in interval notation I have parentheses negative five 24 bracket. So this becomes my union of the two intervals and you can see that this aligns with answer choice C. So hopefully this video helped and see you next time

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